Question 1172615: You have $30,000 to invest in two stock funds. The first fund pays 5% annual interest and the second pays 8% annual interest. If after a year you have made $2,100 interest. How much money did you invest in each account?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788)   (Show Source):
You can put this solution on YOUR website! .
You may start from these two equations
x + y = 30000 (1) (total money)
0.05x + 0.08y = 2100 (2) (total interest)
You then reduce it to one single equation
0.05x + 0.08*(30000-x) = 2100.
I leave it to you to complete the solution from this point.
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It is a standard and typical problem on investments.
If you need more details, or if you want to see other similar problems solved by different methods, look into the lesson
- Using systems of equations to solve problems on investment
in this site.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is a quick and easy way to solve "mixture" problems like this, if a formal algebraic solution is not required.
(1) $2100 interest on an investment of $30,000 is a return of 7%.
(2) 7% is 2/3 of the way from 5% to 8%. (view the three percentages on a number line, if it helps....)
(3) Therefore, 2/3 of the total investment was at the higher rate.
ANSWER: 2/3 of $30,000, or $20,000, was invested at 8%; the other $10,000 at 5%.
CHECK: .08(20,000)+.05(10,000) = 1600+500 = 2100
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